Whether thought of as an emotional weapon, a psychological state or simply the most profoundly irritating behavior that a colleague or family member can manifest, passive aggression is a fancy name for something we are all familiar with. The term dates to 1945, when it was used by the military psychiatrist William Menninger to define the attitude of sulky, balky soldiers.

But passive aggression, as a sly and infuriating art, has surely never been practiced as entertainingly as it is in a certain high school faculty lounge in Garrison, Ohio, where a group of teachers are doing their teeth-gritting darnedest to get along. Such is the setting for “Miles for Mary,” a priceless portrait of accumulating anger in the workplace from the Mad Ones, which opened on Monday at Playwrights Horizons.

First staged at the Bushwick Starr in Brooklyn in the fall of 2016, “Miles for Mary” unfolds as a series of meetings, held over several months in the late 1980s, to organize a local annual telethon for sports scholarships. (The well-worn, cluttered gym room in which they assemble, designed by Amy Rubin, exudes the claustrophobia of the too-familiar.) Like many office meetings, they are conducted according to specific rules of order.

These have been established to keep the participants from speaking out of turn, dominating the proceedings at the expense of others, and generally acting “inappropriately,” to use an enduring, catchall catchword. Psychological safety valves have been set up — under a rubric that includes, in addition to that kindergarten standby “timeout,” “take a two” and “real-time check-in” — to allow for the release and defusing of tensions.

As anyone knows who regularly participates in that most infernal of time-devouring sessions, the staff meeting, such devices have a way of transforming group encounters into pressure cookers. Putting a jargon-laden lid on aggressive behavior pretty much guarantees that the lid is eventually going to blow.

Created by the Mad Ones’ ensemble members and its director, Lila Neugebauer, “Miles for Mary” is both a happy product of and a ruthless portrait of the collaborative process. It also turns out to present a most ingenious acting challenge, in which rage and resentment may be expressed only indirectly.

The cast members, all first-rate, wear Ásta Bennie Hostetter’s 1980s costumes with discomfiting comfort, as if they had no idea how unflattering they were. And they embody creeping disharmony with a smooth synchronicity that any athletic team would envy.

They are Marc Bovino, Joe Curnutte, Michael Dalto, Stephanie Wright Thompson and Stacey Yen. And, oh yes, Amy Staats, whose housebound character is more often heard than seen (through a speaker phone), adding an extra piquancy to the problems of communication.

Setting the show in the 1980s — with attendant mockable cultural references (Chuck Norris, Genesis) — means “Miles for Mary” could easily have been a stretched-out satirical sketch. It’s a danger compounded by its portrayal of teachers who speak to one another in the training-session watchwords and slogans they might use to instruct their students. (“Be Positive. Don’t Panic.” “Mean what you say, say what you mean.”)

Yet even more than when I saw it in 2016, this production slides from surface comedy into an unexpected realm of emotional substance, where laughter increasingly comes with a catch in its throat. You register the obvious jokes in each character — the rah-rah gym teachers, the eager disseminator of cheer and calm, the seething milquetoast. But, little by little, you catch glimpses of fraught, often lonely lives hidden behind the caricatures.

Only glimpses, mind you. “Miles for Mary” includes one (fabulous) climactic explosion. But it doesn’t traffic in big reveals. The same set of rules intended to keep the teachers working together smoothly forestalls confrontational confession. These folks need to use their imaginations to express how they really feel, whether by impatiently tapping a ringed finger on the back of a chair or blurting out a sideways remark (oops!) about one couple’s marital instability.

This makes everyone in this 110-minute show incredibly annoying, and also somehow all the more affecting. Irritation, it seems, has its own special cathartic value in theater.